A soft drink bottler purchases glass bottles from a vendor. The bottles are required to have an internal pressure of at

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A soft drink bottler purchases glass bottles from a vendor. The
bottles are required to have an internal pressure of at least 150
pounds per square inch (psi). A prospective bottle vendor claims
that its production process yields bottles with a mean internal
pressure of 157 psi and a standard deviation of 3 psi. The bottler
strikes an agreement with the vendor that permits the bottler to
sample from the production process to verify the claim. the bottler
randomly selects 60 bottles from the last 10000 produced, measures
the internal pressure of each, and finds the mean pressure for the
sample to be 0.8 psi below the process mean cited by the
vendor.
(a) Assuming that the vendor is correct in his claim, what is
the probability of obtaining a sample mean this far or farther
below the process mean?
(b) If the standard deviation were 3 psi as claimed, but the
mean was 156 psi, what is the probability of obtaining a sample
mean of 156.2 psi or below?
(c) If the process mean were 157 psi as claimed, but the
standard deviation was 3.9 psi, what is the probability of
obtaining a sample mean of 156.2 psi or below?